Review for Exam #1
The exam is on Wednesday, February 29, 2012. Calculators may be used.
Questions will reflect the emphasis of examples done in class, and quiz and
homework questions.
Topics
The exam will cover the following sections of the text:
•
Functions: 0.1–0.6.
•
The derivative: 1.1–1.4, 1.6–1.8.
•
Applications of the derivative: 2.1–2.7.
Review questions for exam #1
(1) Let
p
(
x
) =
x
5

2
x
+ 1 and let
q
(
x
) = (
x
3
+ 2)
2
. Compute
(a)
q
(

1)
(b)
q
(
a
+
b
)
(c)
p
(
q
(

1))
(d)
q
(
p
(
x
))
(2) Find the equation of the straight line through the points (5
,
4) and
(7
,
0).
(3) Find the points of intersection of the curves
y
=
x
3
+2
x
and
y
= 3
x
2
.
(4) Using the definition of the derivative as a limit, compute
f
0
(
x
) if
f
(
x
) =
x
2

3
x
+ 2.
(5) Find the equation of the tangent line to
y
=
x
2

3
x
+ 2 at the point
where
x
=

1.
(6) Find the derivatives of the following functions. You do not have to
simplify your answers.
(a)
f
(
x
) =
x
3
+ 2
x
2
+ 3
x
+ 4.
(b)
f
(
x
) =
7
8
√
x
(c)
f
(
x
) =
√
x
3
+ 2
x
2
3
(d)
f
(
x
) = (
x

2)(
x
+ 2)
(e)
f
(
x
) = ((6
x
+ 5)
4
+ 3)
2
(7) Let
f
(
x
) =
1
3
x
3

3
2
x
2
+ 2
x
+ 4. Find the regions on which
(a)
f
is decreasing
(b)
f
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 Spring '12
 randall
 Calculus, Optimization, dy, 250 ft, 500 ft

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